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#1 2009-11-06 04:05:53

Vercingetorix
Member
Registered: 2009-11-03
Posts: 21

Limit Proof Help

I am trying to prove:

,

by using the method where if given any negative number M, we can find a number

such that

satisfies
if
.

So we begin with

and
.

The text gives an answer of

.

I can't quite get this to work out and feel that the signs are giving me some trouble.  Can anyone show me what's happening here?

Cheers.

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#2 2009-11-06 04:15:08

Vercingetorix
Member
Registered: 2009-11-03
Posts: 21

Re: Limit Proof Help

I have tried to solve it this way:

which is different than

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#3 2009-11-06 05:05:59

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Limit Proof Help

M is negative, it should be

Not

Last edited by TheDude (2009-11-06 05:06:16)


Wrap it in bacon

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#4 2009-11-06 05:13:07

Vercingetorix
Member
Registered: 2009-11-03
Posts: 21

Re: Limit Proof Help

OK, so if you just use an unsigned M...

As soon as I try to take the square root (twice) of

Don't I have a problem since I can't come up with a real value for a negative number?  If the -1 and M cancel out the negatives, how do I arrive at an answer of

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#5 2009-11-06 05:45:42

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Limit Proof Help

It's been stipulated that M < 0, so


Wrap it in bacon

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#6 2009-11-06 05:56:49

Vercingetorix
Member
Registered: 2009-11-03
Posts: 21

Re: Limit Proof Help

I agree with this also, though I don't know how to arrive at the final answer posted above: 1 / (-M)^1/4.  Can you show me how you would solve?

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#7 2009-11-06 06:19:05

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Limit Proof Help


Wrap it in bacon

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#8 2009-11-06 06:25:36

Vercingetorix
Member
Registered: 2009-11-03
Posts: 21

Re: Limit Proof Help

OK, thank you.  I guess I am just having trouble with the signs when raised to a fractional power, but this helps me to understand a little better.  Watch this space - I'm sure that there will be more questions.

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#9 2009-11-06 06:36:17

Sarah12
Guest

Re: Limit Proof Help

I know you are happy to find the answer.:)

#10 2009-11-06 08:10:13

Vercingetorix
Member
Registered: 2009-11-03
Posts: 21

Re: Limit Proof Help

Happy as happy can be.

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